Phase-matching properties of a P1 symmetry crystal, (-)-1-(4-dimethylaminophenyl)-2-(2-hydropropylamino) cyclobutene-3,4-dione, are theoretically and experimentally investigated. The nonlinear-optical coefficients d(ij) are calculated by the oriented-gas model and the effective coefficients are estimated to be 243 pm/V and 23 pm/V at a fundamental wavelength of 1064 nm for the type I and the type II phase-matching of the second-harmonic generation, respectively. The experimental results of the type II second-harmonic generation using the largest plane of the as-grown crystal are given.